Page 231 - FULL FINAL HANDBOOK 20232024

Faculty of Science Handbook, Academic Session 2023/2024

SIF1016 MECHANICS I (2 CREDITS)

Introduction to classical dynamics; Analysis of motion of single particle (Newton’s laws of motion,
equation of motion, conservation principle, linear momentum, forces depend on time, velocity,
force depends on position, work-energy theorem, potential function, simulation of practical
examples); Oscillation ( simple harmonic oscillation, phase diagram, damped oscillation, forced
oscilation, simulation/demonstration of oscillation in various systems); Central forces (reduced
mass, equation of orbital motion, effective potential, qualitative analysis, planetary motion and
Kepler’s laws, gravitational force, stability of circular orbit, orbital mechanics, satellite orbits,
search for exoplanets); Dynamics of system of particles (center of mass, example of motion in
center of mass coordinates, elastic collision, inelastic collision, Rutherford scattering, simulation
of collisions); Motion of systems with variable mass( equation of motion, rocket equation,
simulation of rocket-like motion in various real world systems)

Assessment Method:
Final Examination: 60%
Continuous Assessment: 40%

SIF1017 MATHEMATICAL METHODS I (3 CREDITS)

Differentiation: Differentiation from first principle: products; the chain rule; quotients; implicit
differentiation; logarithmic differentiation; Leibnitz’ theorem; special points of a function;
curvature; theorems of differentiation

Integration: Integration from first principles: the inverse of differentiation; by inspection;
sinusoidal functions; logarithmic integration; using partial fractions; substitution method;
integration by parts; reduction formulae; infinite and improper integrals; plane polar coordinates;
integral inequalities; applications of integration

Complex number: Real and imaginary parts of complex number; complex plane; complex
algebra; complex infinite series; complex power series; elementary functions of complex
numbers; Euler’s formula; powers and roots of complex numbers; exponential and trigonometric
functions; hyperbolic functions; logarithms; complex roots and powers; inverse trigonometric
and hyperbolic functions;

Matrices and solutions for sets of linear equations: matrix and row reduction; Cramer’s rule;
vectors and their notation; matrix operations; linear combinations, linear functions, linear
operators; matrix operators, Linear transformation, orthogonal transformation, eigen value and
eigen vector and diagonalization of matrices; special matrices.

Partial differentiation: power series in two variables; total differentials; chain rule; implicit
differentiation; stationary values of a function with one variable and two variables; application
of partial differentiation to maximum and minimum problems including constraints; Lagrange
multipliers, endpoint and boundary point problems; change of variables; differentiation of
integrals, Leibniz rule.

Assessment Method:
Final Examination: 60%

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